Question

vwxy ~ hgfe. what are m∠v and m∠y?
(images of two quadrilaterals vwxy and hgfe, with angle at w being 85°, angle at e being 109°, angle at h being 96°, angle at f being 70°)
m∠v = \boxed{\space}°
m∠y = \boxed{\space}°

Explanation:

Step1: Use the property of similar polygons

Similar polygons have corresponding angles equal. Since \(VWXY\sim HGEE\), \(\angle V\) corresponds to \(\angle H\). So \(m\angle V = m\angle H\).

Step2: Calculate \(m\angle Y\)

The sum of interior angles of a quadrilateral is \(360^{\circ}\). For quadrilateral \(VWXY\) (or \(HGEE\) as they are similar), we know \(m\angle W = 85^{\circ}\), \(m\angle V=96^{\circ}\), and if we consider the corresponding angles ( \(m\angle X\) corresponds to \(m\angle E = 109^{\circ}\)). Let \(m\angle Y=x\). Then \(85 + 96+109+x=360\).
Simplify the left - hand side: \(290+x = 360\).
Subtract 290 from both sides: \(x=360 - 290\).

Answer:

\(m\angle V = 96^{\circ}\)
\(m\angle Y=70^{\circ}\)